Near-shore scheduling optimization under emission control area and shore power policies: Two-stage distributionally robust model

The implementation of sulfur emission control area (sECA) policies has significantly complicated nearshore scheduling activities for ships. Given the intrinsic linkage between scheduling and berthing processes, this study proposes an integrated research framework that unifies these two stages. To address the uncertainty in berthing time, a two-stage distributionally robust optimization model based on the Wasserstein metric is developed. Dual equivalence and regularization techniques are applied to simplify the model structure, enhancing computational feasibility. For large-scale scenarios, a multi-stage approximation algorithm is designed by integrating deep reinforcement learning with Newton’s method, ensuring efficient solution performance. Validation through simulation experiments based on Nordic North Sea port scenarios confirms the effectiveness of the proposed strategy. Case studies reveal several key insights: under strict time window constraints, ships tend to adopt low-speed sailing strategies; response strategy selection is influenced by fuel consumption and load conditions, with large ships showing a preference for scrubber installation; and under uncertainty, ships prioritize berths equipped with shore power. This research provides theoretical support for promoting the green transformation of shipping operations, offering actionable insights for optimizing nearshore scheduling under emission control regulations.